Geometrie-Viereck-Trapez


  • $A = \frac{a+c}{ 2}\cdot h$
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    $a = \frac{2\cdot A}{ h} - c$
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    $c = \frac{2\cdot A}{ h} - a$
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    $h = \frac{2\cdot A}{a+c}$
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Beispiel Nr: 03
$ \text{Gegeben:}\\\text{Grundlinie c} \qquad c \qquad [m] \\ \text{Grundlinie} \qquad a \qquad [m] \\ \text{Fläche} \qquad A \qquad [m^{2}] \\ \\ \text{Gesucht:} \\\text{Höhe} \qquad h \qquad [m] \\ \\ h = \frac{2\cdot A}{a+c}\\ \textbf{Gegeben:} \\ c=2\frac{2}{5}m \qquad a=2m \qquad A=20m^{2} \qquad \\ \\ \textbf{Rechnung:} \\ h = \frac{2\cdot A}{a+c} \\ c=2\frac{2}{5}m\\ a=2m\\ A=20m^{2}\\ h = \frac{2\cdot 20m^{2}}{2m+2\frac{2}{5}m}\\\\h=9\frac{1}{11}m \\\\\\ \small \begin{array}{|l|} \hline c=\\ \hline 2\frac{2}{5} m \\ \hline 24 dm \\ \hline 240 cm \\ \hline 2,4\cdot 10^{3} mm \\ \hline 2,4\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline a=\\ \hline 2 m \\ \hline 20 dm \\ \hline 200 cm \\ \hline 2\cdot 10^{3} mm \\ \hline 2\cdot 10^{6} \mu m \\ \hline \end{array} \small \begin{array}{|l|} \hline A=\\ \hline 20 m^2 \\ \hline 2\cdot 10^{3} dm^2 \\ \hline 2\cdot 10^{5} cm^2 \\ \hline 2\cdot 10^{7} mm^2 \\ \hline \frac{1}{5} a \\ \hline 0,002 ha \\ \hline \end{array} \small \begin{array}{|l|} \hline h=\\ \hline 9\frac{1}{11} m \\ \hline 90\frac{10}{11} dm \\ \hline 909\frac{1}{11} cm \\ \hline 9090\frac{10}{11} mm \\ \hline 9090909\frac{1}{11} \mu m \\ \hline \end{array}$